Embedded Model Control: Outline of the theory

Local orbital frame predictor for LEO drag-free satellite

“…The direct LORF measurement, being not compliant according to (7), justifies a real-time filter for recovering requirements with some margin. The filter will be designed in the form of a state observer around a stylized discretetime dynamics called embedded model, as suggested in [4].…”

“…The embedded model according to [4] consists of two interconnected parts: the controllable and the disturbance dynamics. Here we prefer avoiding the term`controllable' and replacing it with`orbit', since no orbit control is treated.…”

“…It is related to the model output y m in (22) by the model error e=y−y m , which according to [4] is the composition of the open-loop error dynamics *P(y m , . .…”

“…The approach adopted here follows the embedded model technique [4]: it starts from an accurate model of the orbit (or controllable) dynamics including eccentricity and J 2 gravity term, which is completed by a disturbance dynamics in charge of estimating model uncertainties and simplifications, neglected gravity anomalies and drag-free control residuals. Key steps are the selection of the disturbance dynamic order, of the size and location of the driving noise.…”

The four-tank control problem: Comparison of two disturbance rejection control solutions

“…As a second extension, control algorithms are directly designed in the discrete-time domain on the basis of the so called embedded model, which is a kind of internal model at the core of the control unit. According to the Embedded Model Control (EMC, [25], [26]) methodology, embedded model must include suitable disturbance dynamics (not necessarily first order as in ESO and ADRC), which is driven by arbitrary bounded signals playing the role of driving noise. Model endowment with disturbance dynamics is a key tool for decoupling control strategies as shown in [27] and [28].…”